Exercise 16 Page 815

Since the inscribed angle — which measures 59^(∘) — intercepts the arc that measures a^(∘), we can say that 59 is half of a. 59=a/2 ⇔ a=118

Thus, the value of a is 118.

Finding b

The sum of interior angles of a triangle is 180^(∘). Using this fact, we can find the value of b.

Let's add the angle measures of the triangle. b+59+72=180 ⇔ b=49

Thus, the value of b is 49.

Finding c

By the Inscribed Angle Theorem, we can find the value of c.

Since the inscribed angle — which measures 72^(∘) — intercepts the arc that measures c^(∘), we can say that 72 is half of c.

72=c/2 ⇔ c=144

Therefore, the value of c is 144.

Finding d

Earlier we found that b is 49^(∘). Notice that 49^(∘) is the inscribed angle intercepting the arc that measures d^(∘).

According to the Inscribed Angle Theorem, the measure of an inscribed angle is half the measure of its intercepted arc. This means that 49 is half of d.

49=d/2 ⇔ d=98

Therefore, the value of d is 98.